Fusion category

In mathematics, a fusion category is a category that is abelian, $k$-linear, semisimple, monoidal, and rigid, and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field $$k$$ is algebraically closed, then the latter is equivalent to $$\mathrm{Hom}(1,1)\cong k$$ by Schur's lemma.

Examples

 * Representation Category of a finite group

Reconstruction
Under Tannaka–Krein duality, every fusion category arises as the representations of a weak Hopf algebra.